Difference between revisions of "Twin lattice"
From Online Dictionary of Crystallography
| Line 1: | Line 1: | ||
<Font color="blue"> Réseau de la macle</Font> (''Fr'') <Font color="black"> Reticolo del geminato </Font>(''It'') | <Font color="blue"> Réseau de la macle</Font> (''Fr'') <Font color="black"> Reticolo del geminato </Font>(''It'') | ||
| − | A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. | + | A [[twin operation]] overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent ([[twinning (effects of)]]. The (sub)lattice that is formed by the (quasi)restored nodes is the ''twin lattice''. In case of non-zero [[twin obliquity]] the twin lattice suffers a slight deviation at the composition surface. |
| + | |||
| + | Let H* = ∩<sub>i</sub>H<sub>i</sub> be the intersection group of the individuals in their respective orientations, D(H*) the holohedral supergroup (proper or trivial) of H*, D('''L'''<sub>T</sub>) the point group of the twin lattice and D('''L'''<sub>ind</sub>) the point group of the individual lattice. D('''L'''<sub>T</sub>) either coincides with D(H*) (case of zero [[twin obliquity]]) or is a proper supergroup of it (case of non-zero [[twin obliquity]]): it can be higher, equal or lower than D('''L'''<sub>ind</sub>). | ||
| + | *When D('''L'''<sub>T</sub>) = D('''L'''<sub>ind</sub>) and the two lattices have the same orientation, twinning is by [[twinning by merohedry|merohedry]] ([[twin index]] = 1). When at least some of the symmetry elements of D('''L'''<sub>T</sub>) are differently oriented from the corresponding ones of D('''L'''<sub>ind</sub>), twinning is by [[twinning by reticular polyholohedry|reticular polyholohedry]] ([[twin index]] > 1, [[twin obliquity]] = 0) or reticular pseudopolyholohedry ([[twin index]] > 1, [[twin obliquity]] > 0). | ||
| + | *When D('''L'''<sub>T</sub>) ≠ D('''L'''<sub>ind</sub>) twinning is by [[twinning by pseudomerohedry|pseudomerohedry]] ([[twin index]] = 1, [[twin obliquity]] > 0), [[twinning by reticular merohedry|reticular merohedry]] ([[twin index]] > 1, [[twin obliquity]] = 0) or [[twinning by reticular pseudomerohedry|reticular pseudomerohedry]] ([[twin index]] > 1, [[twin obliquity]] > 0). | ||
| − | |||
==Related articles== | ==Related articles== | ||
[[Mallard's law]] | [[Mallard's law]] | ||
| + | |||
| + | ==History== | ||
| + | The definition of twin lattice was given in: Donnay, G. ''Width of albite-twinning lamellae'', Am. Mineral., '''25''' (1940) 578-586, where the case D('''L'''<sub>T</sub>) ⊂ D('''L'''<sub>ind</sub>) was however overlooked. | ||
==See also== | ==See also== | ||
Revision as of 10:57, 7 May 2006
Réseau de la macle (Fr) Reticolo del geminato (It)
A twin operation overlaps both the direct and reciprocal lattices of the individuals that form a twin; consequently, the nodes of the individual lattices are overlapped (restored) to some extent (twinning (effects of). The (sub)lattice that is formed by the (quasi)restored nodes is the twin lattice. In case of non-zero twin obliquity the twin lattice suffers a slight deviation at the composition surface.
Let H* = ∩iHi be the intersection group of the individuals in their respective orientations, D(H*) the holohedral supergroup (proper or trivial) of H*, D(LT) the point group of the twin lattice and D(Lind) the point group of the individual lattice. D(LT) either coincides with D(H*) (case of zero twin obliquity) or is a proper supergroup of it (case of non-zero twin obliquity): it can be higher, equal or lower than D(Lind).
- When D(LT) = D(Lind) and the two lattices have the same orientation, twinning is by merohedry (twin index = 1). When at least some of the symmetry elements of D(LT) are differently oriented from the corresponding ones of D(Lind), twinning is by reticular polyholohedry (twin index > 1, twin obliquity = 0) or reticular pseudopolyholohedry (twin index > 1, twin obliquity > 0).
- When D(LT) ≠ D(Lind) twinning is by pseudomerohedry (twin index = 1, twin obliquity > 0), reticular merohedry (twin index > 1, twin obliquity = 0) or reticular pseudomerohedry (twin index > 1, twin obliquity > 0).
Related articles
History
The definition of twin lattice was given in: Donnay, G. Width of albite-twinning lamellae, Am. Mineral., 25 (1940) 578-586, where the case D(LT) ⊂ D(Lind) was however overlooked.
See also
Chapter 3.3 of International Tables of Crystallography, Volume D